Method of and system for generating feasible, profit maximizing requisition sets

I claim:

1. In a computer, a method of and system for generating feasible, profit maximizing requisition sets for products purchased under a variety of discount regimes, the method comprising the steps of:

a) specifying by user input to said computer the type of analysis to be run, the controlling forecast, target customer service levels, minimum capital levels and the primary source of historical transaction, forecast element specification and current balance information, user input, electronic files or a basic financial system database,

b) specifying by user input to said computer a plurality of templates and data definitions for use in extracting, converting and storing data from the primary source,

c) extracting, converting and storing the source data in the application database of the present system in a format suitable for use in the present system,

d) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the extracted source data to create, display and store forecasts of sales by account, sales by customer group, sales by item, cash receipts by account as a function of sales by account and cash receipts by customer group as a function of sales by customer group,

e) generating and storing a variable with each forecast element that is calculated in accordance with system default or user specified weighting criteria that facilitates forecast synchronization and obsolescence risk reduction,

f.) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the forecasts of sales by account, sales by customer group and sales by item, cash receipts by account and cash receipts by customer group to create and store a multivalent composite forecast of sales and of cash receipts,

g) using the stored variable for each forecast element to prioritize and quantify the adjustments made to each forecast element in the sales by account, sales by customer group, sales by item, cash receipt by account and cash receipt by customer group forecasts as they are adjusted to exactly match the controlling forecast designated by the user,

h) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to said sales by item forecast and item balance information to create a set of preliminary requisitions for all items that satisfy forecast demand with current vendors and units of measure while maintaining user specified service level targets,

i) calculating the profit maximizing requisition set for all items under a variety of discount regimes within the constraints on vendor and unit of measure substitution established by the user,

j) applying a set of prescribed mathematical algorithms as implemented by a computer program stored in the computer system, to account history information and said forecast of sales by account to create a forecast of expenses by account as well as a balance sheet account balance forecast for use in a financial forecast,

k) creating and displaying a financial forecast on the computer system in the format specified by the user,

l) determining if the forecast financial situation of the commercial enterprise provides for sufficient funds to purchase the profit maximizing set of requisitions (steps a-p are repeated until this condition is satisfied),

m) calculating potential profit enhancing requisition sets for specific items under a variety of discount regimes, within the forecast financial constraints after relaxing user specified restrictions on global vendor and unit of measure substitution,

n) creating and then displaying on the computer system a listing of the potential profit enhancing changes to the profit maximizing requisition set listed in descending capital efficiency order,

o) specifying by user input to said computer the specific profit enhancing changes that are to be included in the profit maximizing requisition set,

p) displaying on the computer system a report that summarizes the final profit maximizing requisition set and the forecast inventory status, and

q) optionally printing financial management and requisition summary reports.

2. The method as recited in claim 1 wherein said step calculating the profit maximizing requisition set for all items under a variety of discount regimes includes the steps of:

a) determining a profitability equation and a set of constraints for the forecast time period for each item quantity discount item using extracted source data,

b) maximizing said profitability equation for each item quantity discount item with a multi-objective, mixed integer, linear programming technique,

c) determining a profitability equation and a set of constraints for the business volume discount time period for the business volume discount items using extracted source data,

d) maximizing said profitability equation for business-volume discount commitment purchases and business-volume discount as-ordered purchases with a multi-objective, mixed integer, linear programming technique, and

e) adjusting the vendor, unit of measure and quantity mix of any preliminary requisitions for business volume discount items that exist for the period between the end of the business volume discount time period and the end of the forecast time period to match the mix of actual and planned purchases during the business volume discount time period.

3. The method as recited in claim 1 wherein said step calculating a profit enhancing set of requisitions for items under a variety of discount regimes includes the steps of:

a) determining a profitability equation and a set of constraints for the forecast time period for each item quantity discount item using extracted source data after removing the specified global vendor and/or unit of measure constraints,

b) maximizing said profitability equation for each item quantity discount item with a multi-objective, mixed integer, linear programming technique,

c) determining a profitability equation and a set of constraints for the business volume discount time period for the business volume discount items using extracted source data after removing the specified global vendor and/or unit of measure constraints,

d) maximizing said profitability equation for business-volume discount commitment purchases and then the business-volume discount as-ordered purchases with a multi-objective, mixed integer, linear programming technique, and

e) adjusting the vendor, unit of measure and quantity mix of any preliminary requisitions for business volume discount items that exist for the period between the end of the business volume discount time period and the end of the forecast time period to match the mix of actual and planned purchases during the business volume discount time period.

4. The method as recited in claim 1 wherein the user has the ability to specify restrictions on vendor and unit of measure substitution during profit maximization calculations both globally and at the item level.

5. The method as recited in claim 1 wherein the user has the ability to specify an obsolescence date and a successor item for items that are expected to become obsolete during the forecast time period.

6. The method as recited in claim 1 wherein said forecasts of sales by account, sales by customer group, sales by item, and expenses by account are calculated using either user specified computation algorithms or weighted averages of the best fit forecasts where the weightings are determined in accordance with a preprogrammed multivalent weighting criteria.

7. In a computer, a method of and system for generating, displaying and storing forecasts of the type used in inventory management and financial planning, the method comprising the steps of:

a) specifying by user input to said computer the type of forecast to be run and the primary source of historical transaction, forecast element specification and current balance information, user input, electronic files or a basic financial system database,

b) specifying by user input to said computer a plurality of templates and data definitions for use in extracting, converting and storing data from the primary source,

c) extracting, converting and storing the source data in the application database of the present system in a format suitable for use in the present system,

d) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the extracted source data to create, display and store forecasts of sales by account, sales by customer group, sales by item, cash receipts by account as a function of sales by account and cash receipts by customer group as a function of sales by customer group,

e) generating and storing a variable with each forecast element that is calculated in accordance with system default or user specified weighting criteria that facilitates forecast synchronization and obsolescence risk reduction,

f) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the forecasts of sales by account, sales by customer group and sales by item, cash receipts by account and cash receipts by customer group to create and store a multivalent composite forecast of sales and of cash receipts, and

g) using the stored variable for each forecast element to prioritize and quantify the adjustments made to each forecast element in the sales by account, sales by customer group, sales by item, cash receipt by account and cash receipt by customer group forecasts as they are adjusted to exactly match a controlling forecast designated by the user or entered by the user into said computer.

8. The method as recited in claim 7 wherein said forecasts of sales by account, sales by customer group, and sales by item are calculated using either user specified computation algorithms or weighted averages of the best fit forecasts where the weightings are determined in accordance with a preprogrammed multivalent weighting criteria.

9. The method as recited in claim 6 wherein said step of specifying the type of analysis to be run provides the user with option of restricting processing to a specific site, department, or division.

10. In a computer, a method of and system for generating, displaying and storing forecasts of the type used for cash management, the method comprising the steps of:

a) specifying by user input to said computer the primary source of historical transaction, forecast element specification and current balance information, user input, electronic files or a basic financial system database,

b) specifying by user input to said computer a plurality of templates and data definitions for use in extracting, converting and storing data from the primary source,

c) extracting, converting and storing the source data in the application database of the present system in a format suitable for use in the present system,

d) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the extracted source data to create, display and store multivalent forecasts of sales by account, sales by customer group, sales by item, cash receipts by account as a function of sales by account and cash receipts by customer group as a function of sales by customer group,

e) generating and storing a variable with each forecast element that is calculated in accordance with system default or user specified weighting criteria that facilitates forecast synchronization and obsolescence risk reduction,

f) applying a set of prescribed mathematical algorithms, as implemented by a computer program stored in the computer system, to the forecasts of sales by account, sales by customer group and sales by item, cash receipts by account and cash receipts by customer group to create and store a multivalent composite forecast of sales and of cash receipts,

g) using the stored variable for each forecast element to prioritize and quantify the adjustments made to each forecast element in the sales by account, sales by customer group, sales by item, cash receipt by account and cash receipt by customer group forecasts as they are adjusted to exactly match a controlling forecast designated by the user or entered by the user into said computer

h) calculating and storing the variables that define the mathematical relationship between prior and current period sales and current period cash receipts by customer group,

l) comparing the variables used to calculate the rate of payment by each customer group with previous payment rate variables for the same customer group in order to highlight any decrease in the rate of payment (i.e., percentage of payments made in later periods is increasing), and

m) displaying a listing to the user listing the customer groups that have decreased their rate of invoice payment from prior levels.

Description Submit all comments and votes

BACKGROUND OF THE INVENTION

This invention relates to a method of and system for enhanced inventory management, more particularly, to a system that creates detailed forecasts of sales before generating profit maximizing sets of requisitions and/or manufacturing work-orders that maintain finished goods inventory at the levels required to maintain user-specified service standards, while satisfying the financial constraints forecast by the system and user specified constraints, during the next 1 to 78 time periods.

The effective control of inventory is one of the more difficult problems faced by businesses today. The high cost of capital and storage space combined with the high risk of obsolescence, created by the ever accelerating pace of change in today's economy, drives companies to minimize their investment in inventory. At the same time, unprecedented growth in the number and variety of products, intense global competition and increasing demands for immediate delivery can force companies to increase their inventory investments. Balancing these two conflicting demands while effectively and efficiently considering the different price schedules, volume discounts, quality and lead time options that different vendors and different in-house manufacturing resources offer is a very complex task. The complexity of this task has increased geometrically in recent years.

One of the major causes of this increase in complexity is the unprecedented increase in the number and variety of products in almost every product market from "apparel and toys to power tools and computers.".sup.1 For example, "the number of new product introductions in the U.S. food industry has exploded in recent years from 2,000 in 1980 to 18,000 in 1991.".sup.2 Because the level of total sales to customers has not increased at a level that even remotely approaches the rate at which the number of products has increased, virtually every commercial enterprise selling products, most notably manufacturers, distributors and retailers, has experienced a significant increase in the number of inventory items that must be managed. Complicating matters even further, the increase in the rate of new product introductions has been matched by a corresponding increase in the rate at which old products are discontinued or replaced by new products. This increasing risk of product obsolescence has increased the financial risk associated with inventory management as discontinued products generally have drastically lower market values. Businesses that are left holding products that have been discontinued or replaced are generally forced to take severe markdowns and/or make inventory write-offs that can seriously diminish or even eliminate their working capital.

1. Marshall Fisher, Janice Hammond, Walter Obermeyer, Ananth Raman, "Making Supply Meet Demand in an Uncertain World", Harvard Business Review, May-June 1994, page 83.

2. ibid, page 86.

The difficulties described above are being exacerbated by the increase in complexity caused by vendors that have introduced a variety of new discount schedules and incentives. Traditional purchasing incentives were associated with offering lower prices for larger purchases of a single item. These item-quantity discounts are still widely used by vendors in a variety of industries. New discount options have been created in an effort to enhance the frequency of repeat business by rewarding customers with discounts based on their total level of business during some time period, usually a year, rather than basing discounts solely on the basis of the quantities from a single order as they had done in the past. These business-volume discounts typically offer two different types of discount schedules to the customer. The first being a discount schedule based on the dollar volume purchased during a specified time period. This type of discount schedule is commonly known as an as-ordered discount schedule. Under this type of discount schedule the level of discount rises as the total as-ordered volume increases. An example of this type of discount schedule is shown in Table 1.

TABLE 1 ______________________________________ As-Ordered Discount Schedule Vendor A Vendor B ______________________________________ $0-$20,000 0 0 $20,001-$50,000 0 5% over $50,000 2% 6% ______________________________________

The second type of business-volume discount schedule is typically based on the customer's commitment to purchase a specified volume of a product during a specified time period. The commitment-basis discount schedules typically come in two segments. First, the customer is given a different base price schedule for items purchased when a commitment to buy a certain quantity of the item has been made. The base prices on the commitment-basis price schedule often contain discounts from the as-ordered base prices as shown in Table 2.

TABLE 2 ______________________________________ As-Ordered Vendor-Product Commitment Base Price Base Price ______________________________________ Vendor A - Widget $20.00 $21.00 Vendor A - Carton $5.00 $5.00 Vendor B - Widget $20.50 $22.00 Vendor B - Carton $4.50 $5.00 ______________________________________

Once the customer has purchased a certain amount on a commitment basis, all subsequent orders for that item during the relevant time period will be priced at the commitment price and the customer is said to have "locked in" the commitment price. The second element of the commitment-basis discount is typically a percentage discount based on the cumulative total of commitment purchases made during the relevant time period. An example of this type of commitment-basis discount schedule is shown in Table 3.

TABLE 3 ______________________________________ Commitment Discount Schedule Vendor A Vendor B ______________________________________ $0-$10,000 0 0 $10,001-$25,000 1% 2% $25,001-$50,000 2% 4% $50,001-$100,000 3% 6% over $100,000 5% 8% ______________________________________

In this environment a customer would have four different possible prices for the purchase of five hundred (500) widgets from the two different business volume discount vendors as shown in Table 4.

TABLE 4 ______________________________________ Vendor A Vendor B ______________________________________ Year to date actual as-ordered $7,012 $19.553 volume - total Current as-ordered discount percentage 0% 0% Widget commitment price locked in? YES NO Widget base price as-ordered $20.00 $22.00 Cost for 500 widgets - as-ordered $10,000 $10,472 Year to date actual committed $28,119 $67,328 purchases - total Current commitment-basis 2% 6% discount percentage Widget commitment-basis price $20.00 $20.50 Cost for 500 widgets - commit- $9,800 $9,635 ment-basis ______________________________________

It is clear from the preceding example that the business volume discount schedules can severely complicate a purchase order decision. In the example shown above the lowest cost alternative for the company is to order from Vendor B on a commitment basis. Thus we see that a customer would have to evaluate the quantity commitments to two vendors, closely monitor the year to date volume for each vendor and evaluate up to four different prices from the two different vendors before placing a single order for a single item. It is also clear from the preceding example that the task of consistently determining the best purchase options for even a small commercial enterprise stocking only a few hundred items can be a daunting task. It is important to note here that the level of complexity shown in this example has been simplified as it ignores the complications that would be introduced by considering different units of measure from the different vendors.

Because of the complexity and risk associated with the inventory management task, it is not uncommon for companies to have several personnel in an operations or purchasing department dedicated to planning, purchasing and controlling inventory investments. In performing their various job functions the operations/purchasing personnel in larger companies typically utilize several different computer based systems for: forecasting demand, planning purchase orders or manufacturing work orders, monitoring the quality and quantity of the items received in the warehouse, tracking returned goods, placing purchase orders, controlling inventory, monitoring costs and entering sales orders. In smaller companies the management of inventory is often accomplished through the use of informal and paper based systems. In some cases the informal systems and the larger "formal" systems are supplemented by microcomputer based spreadsheet programs. In all cases, the goal of the operations/purchasing department is to have the required items in inventory available for sale when the customer orders the product while keeping the investment in inventory as low as possible.

Because inventory is typically the largest component of working capital for companies in the retail, manufacturing and distribution industries, the importance of efficiently managing inventory can not be overemphasized. The significance of effective inventory management practices is particularly high for the small companies that comprise the fastest growing segment of the modem American economy. These small firms typically don't have the working capital required to withstand large mistakes in inventory management. Compelling evidence of the importance of effective inventory management practices is found in the Dun & Bradstreet Business Failure Record that shows inventory investment problems are one of the leading causes of business failure for retail, manufacturing and distribution companies. It is clear from the preceding discussion that a system that helps companies effectively manage inventory could enhance both the short-term financial results and the long-term survival prospects of many companies.

PRIOR ART

To help address some aspects of the complex inventory management problem, inventors have previously created systems for determining the most cost effective method for procuring items under idealized conditions. U.S. Pat. No. 5,224,034 to Katz and Sedrian (1993) discloses an automated system for generating procurement lists that uses linear programming optimization algorithms to generate lists showing the annual volume of each product that is to be purchased from each of the different vendors offering business volume discounts to minimize the cost of acquiring the user specified annual volume. There are several drawbacks and limitations inherent in a system of this type including:

(a) Constantly changing business conditions require that all item forecasts be updated frequently and accurately if the system is to provide truly useful output. Because the system is highly specialized, completing these data inputs requires the error-prone, time consuming and costly conversion of data to the format required by the separate inventory optimization system;

(b) After completing the conversion of data to the system required format, the user is then faced with the costly and time consuming task of re-keying or transferring the data into the separate system;

(c) The specialized, technical nature of the system generally requires the use of a highly-skilled, trained operator to run the systems effectively;

(d) The outputs from the system need to be transferred into the purchasing and/or accounting systems before they can be fully utilized. This transfer often entails the error-prone, time consuming and costly conversion and re-keying of data;

(e) The system has no provision for assuring that the company using the system will have the financial resources required to acquire the items identified on the procurement lists. It does little good to optimize plans for committed and as-ordered purchases if the company will not have sufficient funds to pay for the items ordered when the bills come due;

(f) The determination of optimized inventory purchases is implicitly viewed as an exercise that is separate from the determination of financial constraints (if any) when in fact the two are tightly interrelated. The resources that a company will have available for making future purchases is in part dependent on the discounts it has received for the purchases it has previously made. At the same time, the discounts that a company will receive is a function of the size of the purchases that it can afford to commit to and/or make without running short of funds;

(g) The system has no facility for effectively assessing the impact of impending obsolescence on plans for procuring items. The program may recommend an increase in the purchase quantity for an item from a vendor who is expected to introduce a new version in the near future. The new version could render the older versions of the item obsolete and the cost of writing off the obsolete inventory could very easily outweigh the cost savings realized by optimizing the purchase mix and order quantities;

(h) A limitation that is closely related to the shortcoming discussed in item (g) is that the system has no capability for handling planned product obsolescence. For example, even if it is known that a product is to be phased out on a given date and a new product is to take its place, there is no mechanism available to manage the transition;

(i) The system is severely limited in its usefulness as it only optimizes the mix of items purchased under business volume discount regimes. Most companies have more than one type of discount available from their different vendors. Indeed, some vendors offer more than one type of discount. The discount options may include: quantity discounts for individual items, volume discounts based on the total committed volume or volume discounts based on the total ordered volume or some combination of the two or on purchases of specific product mixes or product combinations. As a result, companies that were seeking to optimize the purchase of all of their products would be forced to incur the time, effort and expense required to install and maintain multiple inventory optimization systems;

(j) The system only minimizes the cost of purchasing items forecast by the user under the user-defined constraints. In some cases the user-defined constraints impose artificial limitations on the solutions developed by the system. Limiting the system to purchase only the commitment levels and quantities forecast by the user is an artificial constraint that generally has no basis in reality. In reality, the suppliers (internal or external) can probably provide whatever quantities the user chooses to order and can afford to pay for. In some cases ordering more than the forecast requirements can produce significant savings. As shown in the following example, committing $10 more than permitted under the user specified constraints to a specific vendor would increase pre-tax profitability by $40,000:

______________________________________ Committed $ Volume Discount % ______________________________________ $0 to $999,999 0 $1 M to $1,999,999 2 $2 M to 2,999,999 4 ______________________________________

Total 12 month $ Volume Forecast Vendor A=$2,499,987.50

Maximum percentage of forecast volume that can be committed=80%

Vendor A Dollar Commitment=$1,999,990.00

Increase in discount percentage from increasing commitment by $10=2%

Savings from increased discount=$2,000,000.times.2%=$40,000

This enormous potential profit would not be highlighted to the user by a system that simply minimized costs within the constraints established by the user. Clearly, a system that isn't artificially restricted to solutions that include the forecast item demand limitations can provide substantial benefits to the user;

(k) The system only minimizes costs and doesn't maximize the profitability of the firm using the system. The primary goal of most firms is not to minimize costs rather it is to realize as large a profit as possible. The example shown below illustrates how significant this change in focus can be when combined with the removal of the artificial constraints discussed in item (j). Consider a profit maximization model with three products and three resources. A traditional linear programming model for the specific situation would be:

Maximize profit: p=80x.sub.1 +32x.sub.2 +57.6x.sub.3

Subject to:

6.4x.sub.1 +4.82x.sub.2 +3.84x.sub.3 .ltoreq.1,280 (resource 1)

3.2x.sub.1 +4.8x.sub.2 +6.4x.sub.3 .ltoreq.1,600 (resource 2)

3.2x.sub.1 +3.2x.sub.2 +3.2x.sub.3 .ltoreq.960 (resource 3)

x.sub.1, x.sub.2, x.sub.3 .gtoreq.0

Using the simplex method, the optimal solution is reached at x.sub.1 =228.576, x.sub.2 =0.0, x.sub.3 =685.728 and p=$57,784.01. If the prices of the resources were s.sub.1 =$20, s.sub.2 32 $10 and s.sub.3 =$40 we can use the above constraints to determine the maximum amount that can be purchased: 1,280($20)+1,600($10)+960($40)=$80,000.

If the above problem were changed to the multiple criteria, De-Novo maximization formulation to remove the artificial constraints on purchasing resources, it would appear as shown below:

Maximize profit: p=80x.sub.1 +32x.sub.2 +57.6x.sub.3

Subject to:

2x.sub.1 +1.5x.sub.2 +1.2x.sub.3 .ltoreq.x.sub.4 (resource 1)

x.sub.1 +1.5x.sub.2 +2x.sub.3 .ltoreq.x.sub.5 (resource 2)

x.sub.1 +x.sub.2 +x.sub.3 .ltoreq.x.sub.6 (resource 3)

20x.sub.1 +10x.sub.2 +40x.sub.3 .ltoreq.80,000 (budget)

x.sub.1, x.sub.2, x.sub.3, x.sub.4, x.sub.5, x.sub.6 .gtoreq.0

Solving the above yields the following optimal solution: x.sub.1 =888.896, x.sub.4 =1,777.792, x.sub.5 =888.896, x.sub.6 =888.896 and p=$71,111.68. The optimal solution from this formulation is substantially different from the previous formulation and it has a profit level 23% higher than the one produced by the linear programming model. Clearly, there can be substantial benefits to changing the focus to profit maximization rather than cost minimization while removing constraints that artificially limit the potential solutions;

The next ten (10) shortcomings and limitations of the present system would all contribute to a decision to establish another separate system dedicated to inventory management. This inventory management system would provide the required forecasts, target inventory levels, requisition quantities, requisition dates, stock-out probabilities and projected stock-out costs in a consistent and efficient manner. However, to realize these benefits the user would be required to incur the time, effort and expense associated with setting up and maintaining a separate system for monitoring inventory usage, developing forecasts and managing inventory. The user would also be faced with the costly and time consuming task of re-keying or transferring data into and out of the separate inventory management system.

(l) The system has no simple mechanism for allowing the user to restrict the purchase of an item to a particular vendor. It is not uncommon for a user to have strategic or qualitative reasons for choosing one vendor over another in the purchase of a specific item--even if the price for buying from that vendor is higher. Restricting vendor selection for an item using the system described by Katz & Sedrian would require the user to develop a constraint and enter it into the specialized system before processing begins;

(m) The system has no provision for allowing the user to order items using different units of measure. It is commonplace for a vendor to offer items in different units of measure with different price schedules. If the user wishes to order product using a different unit of measure, then he or she will be forced to go through the costly, time consuming and error-prone effort to convert the procurement lists that have already been created using a different unit of measure. If lower prices are offered for different units of measure that weren't considered, it is entirely possible that the solution developed by the system would not be the lowest cost solution;

(n) The effectiveness of the system in planning the purchases required to keep the proper items stocked in inventory is completely dependent on the demand forecasts developed and input to the system by the user;

(o) The system is limited to planning purchases one year at a time for all business volume items. Because the system doesn't have the ability to analyze shorter or longer forecast time periods, the user will be required to work with another system to address inventory planning needs for any time period other than a year;

(p) The system only determines the annual quantity mix by vendor for the items, the actual dates and order quantities are not determined for any item. The user is required to go through an additional time consuming exercise of determining how large the orders should be and when to place orders;

(q) The system doesn't consider service levels (e.g., fill rate targets where a 95% fill rate is defined to mean that 95% of the total annual demand for an item is supplied by inventory from stock) and demand variability when determining the annual purchase quantities. Ignoring these factors can leave the commercial enterprise using the system vulnerable to inventory stock-outs. Any inventory stock-out would probably cause lost profits for the business when the consumer purchases the item from another supplier that has the item in stock.

The example presented in Tables 5, 6 and 7 illustrates the impact of different levels of item demand variability on the available inventory of two different items with the same total forecast demand, the same average monthly demand and the same fill rate targets.

TABLE 5 ______________________________________ Monthly Demand Part A Part B ______________________________________ Last month 100 55 Two months ago 100 0 Three months ago 100 100 Four months ago 100 20 Five months ago 100 115 Six months ago 100 95 Seven months ago 100 15 Eight months ago 100 0 Nine months ago 100 500 Ten months ago 100 0 Eleven months ago 100 0 Twelve months ago 100 300 Total 12 Month Demand 1,200 1,200 Average Monthly Demand 100 100 Sample Standard Deviation 0 152.5 ______________________________________

TABLE 6 ______________________________________ Part A Part B ______________________________________ Lead Time 2 months 2 months Available Inventory 300 units 300 units Fill Rate - Target % 95% 95% Order Cost $500 $500 Carrying Cost - Annual % 12% 12% Unit Price $50 $50 Economic Order Quantity* 450 450 ______________________________________ *the Economic Order Quantity formula will be detailed later

A system that didn't address the differences caused by the different demand patterns of the two items would use the same re-order level for each item. The re-order level for the parts can be calculated as shown below:

Reorder Level Part A=(100 units/month.times.2 months lead time)=200

As shown in Table 7, if the same re-order level were used for both items and the demand pattern from the prior year was repeated, then the available inventory during the coming year for these two parts would be quite different.

TABLE 7 __________________________________________________________________________ Start Inv Part A A Order End Inv Qty A Start Inv Part B B Order End Inv Qty B Month Part A Demand Receipt Part A Ordered Par B Demand Receipt Part B Ordered __________________________________________________________________________ 1 300 100 0 200 450 300 300 0 0 450 2 200 100 0 100 0 0 0 0 0 0 3 100 100 450 450 0 0 0 450 450 0 4 450 100 0 350 0 450 500 0 -50* 450 5 350 100 0 250 0 -50* 0 0 -50* 0 6 250 100 0 150 450 -50* 15 450 385 0 7 150 100 0 50 0 385 95 0 290 0 8 50 100 450 400 0 290 115 0 175 450 9 400 100 0 300 0 175 20 0 155 0 10 300 100 0 200 450 155 100 450 505 0 11 200 100 0 100 0 505 0 0 505 0 12 100 100 450 450 0 505 55 0 450 0 Total 1,200 1,350 1,350 1,200 1,350 1,350 __________________________________________________________________________ *negative inventory represents a backorder

As shown above, if the timing of the purchases of Part B weren't adjusted to build the inventory to a level that was sufficient to absorb the large variability in monthly demand, then the user would experience a two month